After a close comparison, the mysterious studio Smokestack Lightning is simply the 11/19/66 live version again, but in mono, slowed-down, and faded-out early.
(The same 11/19/66 Smokestack can also be found masquerading as a "2/12/67" studio take.)
The Lovelight is also not from the fall '67 Anthem sessions. It's the longest take from the Lovelight rehearsal session, which was commonly dated 11/19/67. That date is flagrantly wrong, though. After listening to the full rehearsal session, these Lovelights are clearly earlier & more primitive than even the 8/5/67 live version, which is much stronger and more fully developed.
In this studio take, the band are still working out the basic parts - Pigpen sings it a bit differently, Jerry's still figuring out his soloing, and a lot of the sections of the live Lovelights are still missing. So I would guess that the Lovelight session may have taken place in July '67 or so.
The Other One & Alligator>Caution remain safely in the mid-October '67 sessions. Alligator has the drum break that was added after Mickey Hart joined, so it's after 9/29. The Other One sounds stodgy & tentative compared to the live 10/22/67 version, so I think it precedes that.
A better studio take of the Other One suite from these sessions has surfaced as a filler track in this February '71 studio rehearsal: